Question: Find the 3-Part Ratio

Comment on Find the 3-Part Ratio

For the first question - how you divide all parts by c? Wouldn't that get rid of the "c" on the left side of the equation and put a & b over c?

a:b:c=2c:3c:6c
*divide both sides by c*

a/c:b/c:c/c=2:3:6
greenlight-admin's picture

That isn't how EQUIVALENT ratios work.

If we take a ratio (not an equation) and multiply or divide it's PARTS by some non-zero value, we create an EQUIVALENT ratio.

So, for example, we can take the ratio 10 : 35, and divide both parts of the ratio by 5 to get the EQUIVALENT ratio 2 : 7

That is, 10 : 35 = 2 : 7

Likewise, we can take the ratio 2c : 3c : 6c and divide all the parts by c to get 2 : 3 : 6

That is 2c : 3c : 6c = 2 : 3 : 6

So, as the solution tells us...

a : b : c = c/3 : c/2 : c [via substitution]

= 2c + 3c + 6c [we took the previous ratio and multiplied all 3 parts by 6]

= 2 + 3 + 6 [we took the previous ratio and divided all 3 parts by c]

Does that help?

At 1:41 I'm confused as to how you multiply all three terms by 6 to get 2c: 3c:6c. Wouldn't you divide all the 3 terms by 6 to get 2c: 3c: 6c?
greenlight-admin's picture

You're referring to 1:30 in the above video.
Here we must convert c/3 : c/2 : c into an equivalent ratio.

If we multiply each term by 6, we get: 6c/3 : 6c/2 : 6c
When we simplify each term by 6, we get: 2c : 3c : 6c

Now let's see what happens when we DIVIDE each term by 6.
We get: (c/3)/6 : (c/2)/6 : c/6

Rewrite 6 as 6/1 to get: (c/3)/(6/1) : (c/2)/(6/1) : c/(6/1)
Invert and multiply: (c/3)(1/6) : (c/2)(1/6) : c(1/6)
We get: c/18 : c/12 : c/6

While this new ratio is still EQUIVALENT to c/3 : c/2 : c, it doesn't match any of the answer choices.

For more information about eliminating fractional expressions, watch: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Cheers,
Brent

For this question, does this approach make sense?

Since c / a = 3, then a / c = 1 / 3, meaning, a : c = 1 : 3
Similarly, since c / b = 2, then b / c = 1 / 2, meaning, b : c = 1 : 2

To link a : c to b : c, we will use c. The only way we can link c is to make c in both a multiple of both 3 and 2. Here, we will use 6. In the first ratio, we get a : c = 2 : 6 and in the second ratio, we get b : c = 3 : 6. To put it together, we get a : b : c = 2 : 3 : 6.

Did that approach make sense? Thanks fo your time.
greenlight-admin's picture

Hey stomer,

That's a completely valid approach. Nice work!

Cheers,
Brent

Hi, why does the rule 'if a/b = c/d, then ad = bc' not work here? Using this, c/a = 3/1 would give us 1c = 3a, and c/b = 2/1 would give us 1c = 2b, and the ratio of a : b : c would be 1 : 2 : 3 (which is not the correct answer).
greenlight-admin's picture

Everything you stated is entirely true (1c = 3a and 1c = 2b), but what steps did you take to conclude that a:b:c = 1:2:3?
Once I see your solution, I'll be able to help more.

Cheers,
Brent

Sorry, I misspoke above. I meant to say that if 1c = 3a and 1c = 2b, shouldn't the ratio of a : b : c equal 3 : 2 : 1? (a : c is 3 : 1 and b : c is 2 : 1; c is equivalent in both these ratios (1), so joining them together is 3 : 2 : 1.) But this is not the correct answer.
greenlight-admin's picture

Be careful. If 1c = 3a, then a : c = 1 : 3

Here's why.
Take: 1c = 3a
Divide both sides by c to get: 1 = 3a/c
Divide both sides by 3 to get: 1/3 = a/c
In other words, a : c = 1 : 3

Likewise, if 1c = 2b, then b : c = 1 : 2

Cheers,
Brent

Hi Brent,
This is how I worked this problem.

If c/a=3, then c/a = 3/1 (c=3, a=1 )
If c/b=2 , then c/b = 2/1 (c=2, b=1 )

C is a common term in both ratios, so combine them by creating equivalent ratios.

Multiply first ratio by 2 and second one by 3
c/a = 6/2
c/b = 6/3

From the above, a = 2, c=6 and b = 3
So, a:b:c = 2:3:6.

Please let me know if this works :)
greenlight-admin's picture

That approach is perfect. Nice work!

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